It is known that the GFD is invariant to the choice of parametrization [1]}. Thus, as long as one knows the form of \(\psi ^{-1}\)  for a manifold, there is no need for any new theory. However, in practice, such a parameterization may not be known, which is why there is a strong need for (REF ). The CGFD is a more general approach to defining a GFD on a manifold, since it allows for when a constraint can only be written down implicitly.
